I mean... You know... We study certain analytic properties of the ordered and unordered configuration spaces Cn o (X) = {(q1, ..., qn) ∈ X | qi 6= qj ∀ i 6= j} and Cn(X) = {Q ⊂ X | #Q = n} of simply connected algebraic curves X = C and X = CP. For n ≥ 3 the braid group Bn(X) = π1(C(X)) of the curve X is non-abelian. A map F : Cn(X) → Ck(X) is called cyclic if the subgroup F∗(π1(C(X))) ⊂ π1(C(X)...

We prove the conjecture that higher Tamari orders of Dimakis and Müller-Hoissen coincide with first Stasheff-Tamari orders. To this end, we show may be conceived as image an order-preserving map from Bruhat to This is defined by taking cross-section a cubillage cyclic zonotope. provide new proof surjective further full, which entails aforementioned conjecture. explain how maps are full correspo...

I mean... You know... We study certain analytic properties of the ordered and unordered configuration spaces Cn o (X) = {(q1, ..., qn) ∈ X | qi 6= qj ∀ i 6= j} and Cn(X) = {Q ⊂ X | #Q = n} of simply connected algebraic curves X = C and X = CP. For n ≥ 3 the braid group Bn(X) = π1(C(X)) of the curve X is non-abelian. A map F : Cn(X) → Ck(X) is called cyclic if the subgroup F∗(π1(C(X))) ⊂ π1(C(X)...

I mean... You know... We study certain analytic properties of the ordered and unordered configuration spaces Cn o (X) = {(q1, ..., qn) ∈ X | qi 6= qj ∀ i 6= j} and Cn(X) = {Q ⊂ X | #Q = n} of simply connected algebraic curves X = C and X = CP. For n ≥ 3 the braid group Bn(X) = π1(C(X)) of the curve X is non-abelian. A map F : Cn(X) → Ck(X) is called cyclic if the subgroup F∗(π1(C(X))) ⊂ π1(C(X)...

Finite affine groups are given by groups of translations and di- lations on finite cyclic groups. For cyclic groups of prime order we develop a time-scale (wavelet) analysis and show that for a large class of non-zero window signals/vectors, the generated full cyclic wavelet system constitutes a frame whose canonical dual is a cyclic wavelet frame.

Let Ng(f ) denote the number of rooted maps of genus g having f edges. An exact formula for Ng(f ) is known for g = 0 (Tutte, 1963), g = 1 (Arques, 1987), g = 2,3 (Bender and Canfield, 1991). In the present paper we derive an enumeration formula for the number Θγ (e) of unrooted maps on an orientable surface Sγ of a given genus γ and with a given number of edges e. It has a form of a linear com...

Let Ng(f) denote the number of rooted maps of genus g having f edges. Exact formula for Ng(f) is known for g = 0 (Tutte 1963), g = 1 (Arques 1987), g = 2, 3 (Bender and Canfield 1991). In the present paper we derive an enumeration formula for the number Θγ(e) of unrooted maps on an orientable surface Sγ of given genus γ and given number of edges e. It has a form of a linear combination ∑ i,j ci...

An implementation of an out-of-order processing unit based on Tomasulo’s algorithm is formally verified using compositional model checking techniques. This demonstrates that finite-state methods can be applied to such algorithms, without recourse to higher-order proof systems. The paper introduces a novel compositional system that supports cyclic environment reasoning and multiple environment a...